Finite Group Databasebeta

← Group #10706144

Character table — Group #10706144

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222222222244444444444444444444444444444444444444161616161616161616161616242424242424242448484848
order12222234444666666688884444888888121212121212121212121212242424242424242424242424242424244444121212121212121216161616161616162444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111-1-111111111111111-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1
χ61111111-1-111111111111111-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111
χ71111111-1-111111111111111-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111
χ81111111-1-111111111111111-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1
χ91111-1-111111-1-1111-1-1-1-1-1-1-11-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-1i−ii−iii−i−iii−i−iii−i−iii−i−i1-11-1
χ101111-1-111111-1-1111-1-1-1-1-1-1-11-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-1i−ii−iii−i−iii−i−i−i−iii−i−iii-11-11
χ111111-1-111111-1-1111-1-1-1-1-1-1-11-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-1−ii−ii−i−iii−i−iiiii−i−iii−i−i-11-11
χ121111-1-111111-1-1111-1-1-1-1-1-1-11-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-1−ii−ii−i−iii−i−iii−i−iii−i−iii1-11-1
χ131111-1-11-1-111-1-1111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111i−i−iiii−i−i−i−iiiii−i−i−i−iii1-1-11
χ141111-1-11-1-111-1-1111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111i−i−iiii−i−i−i−iii−i−iiiii−i−i-111-1
χ151111-1-11-1-111-1-1111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111−iii−i−i−iiiii−i−iii−i−i−i−iii-111-1
χ161111-1-11-1-111-1-1111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111−iii−i−i−iiiii−i−i−i−iiiii−i−i1-1-11
χ17222222222222222222-2-2-2-22222-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000
χ18222222222-2-222222220000-2-22-2000000-2-222-2-222-2-2-2-200000000000000000000000000002−22−22−22−20000
χ19222222222-2-222222220000-2-22-2000000-2-222-2-222-2-2-2-20000000000000000000000000000−22−22−22−220000
χ202222222-2-2222222222-2-2-2-22-2-2-2-2-2222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-222222222000000000000000000000000
χ212222222-2-2-2-222222220000-22-22000000-2-2-2-222-2-222-2-200000000000000000000000000002−22−2−22−220000
χ222222222-2-2-2-222222220000-22-22000000-2-2-2-222-2-222-2-20000000000000000000000000000−22−222−22−20000
χ23222222-12222-1-1-1-1-1-1-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ24222222-12222-1-1-1-1-1-1-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ25222222-12222-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111111111110000−i3i3−i3i3−i3i3−i3i3000000000000
χ26222222-12222-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111111111110000i3−i3i3−i3i3−i3i3−i3000000000000
χ27222222-1-2-222-1-1-1-1-1-1-122222-2-2-222-2-2-2-2-1-111111111-1-1-1-1-1-1-1-1-1-11111111122-2-2-1-1-1-11111000000000000
χ28222222-1-2-222-1-1-1-1-1-1-122222-2-2-222-2-2-2-2-1-111111111-1-1-1-1-1-1-1-1-1-111111111-2-2221111-1-1-1-1000000000000
χ29222222-1-2-222-1-1-1-1-1-1-1-2-2-2-22-2-2-2-2-22222-1-111111111-1-111111111-1-1-1-1-1-1-1-10000−i3i3−i3i3i3−i3i3−i3000000000000
χ30222222-1-2-222-1-1-1-1-1-1-1-2-2-2-22-2-2-2-2-22222-1-111111111-1-111111111-1-1-1-1-1-1-1-10000i3−i3i3−i3−i3i3−i3i3000000000000
χ312222-2-222222-2-2222-2-22222-22-2-2-2-2-2-222-2-22222-2-2-2-222-2-2-2-22222-2-2-2-22222000000000000000000000000
χ322222-2-2222-2-2-2-2222-2-200002-2-220000002222-2-2-2-222-2-20000000000000000000000000000−i2i2i2−i2−i2i2i2−i20000
χ332222-2-2222-2-2-2-2222-2-200002-2-220000002222-2-2-2-222-2-20000000000000000000000000000i2−i2−i2i2i2−i2−i2i20000
χ342222-2-22-2-222-2-2222-2-22222-2-222-2-222-2-2-2-2-2-2-2-2222222-2-2-2-222222222-2-2-2-2000000000000000000000000
χ352222-2-22-2-2-2-2-2-2222-2-20000222-200000022-2-22222-2-2-2-20000000000000000000000000000−i2i2i2−i2i2−i2−i2i20000
χ362222-2-22-2-2-2-2-2-2222-2-20000222-200000022-2-22222-2-2-2-20000000000000000000000000000i2−i2−i2i2−i2i2i2−i20000
χ372222-2-2-1222211-1-1-1112222-22-2-2-2-2-2-22211-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-100003−3−333−3−33000000000000
χ382222-2-2-1222211-1-1-1112222-22-2-2-2-2-2-22211-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-10000−333−3−333−3000000000000
χ392222-2-2-1222211-1-1-111-2-2-2-2-22-2-22222-2-211-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111112i−2i2i−2i−i−iii−i−iii000000000000
χ402222-2-2-1222211-1-1-111-2-2-2-2-22-2-22222-2-211-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111−2i2i−2i2iii−i−iii−i−i000000000000
χ412222-2-2-1-2-22211-1-1-1112222-2-222-2-222-2-2111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111100003−3−33−333−3000000000000
χ422222-2-2-1-2-22211-1-1-1112222-2-222-2-222-2-2111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111110000−333−33−3−33000000000000
χ432222-2-2-1-2-22211-1-1-111-2-2-2-2-2-22222-2-222111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-12i−2i−2i2i−i−iiiii−i−i000000000000
χ442222-2-2-1-2-22211-1-1-111-2-2-2-2-2-22222-2-222111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1−2i2i2i−2iii−i−i−i−iii000000000000
χ45444444-244-4-4-2-2-2-2-2-2-20000-4-44-400000022-2-222-2-222220000000000000000000000000000000000000000
χ46444444-2-4-4-4-4-2-2-2-2-2-2-20000-44-440000002222-2-222-2-2220000000000000000000000000000000000000000
χ474444-4-4-244-4-422-2-2-22200004-4-44000000-2-2-2-22222-2-2220000000000000000000000000000000000000000
χ484444-4-4-2-4-4-4-422-2-2-2220000444-4000000-2-222-2-2-2-222220000000000000000000000000000000000000000
χ4944-4-4004004-4004-4-40000000000004i−4i0000000000004-4000000004i4i−4i−4i0000000000000000000000000000
χ5044-4-4004004-4004-4-4000000000000−4i4i0000000000004-400000000−4i−4i4i4i0000000000000000000000000000
χ5144-4-400400-44004-4-4004i4i−4i−4i00000000000000000000-4400004i4i−4i−4i00000000000000000000000000000000
χ5244-4-400400-44004-4-400−4i−4i4i4i00000000000000000000-440000−4i−4i4i4i00000000000000000000000000000000
χ5344-4-400-2004-4−2i32i3-222−2i32i300000000004i−4i00−2i32i300000000-2200000000−2i−2i2i2i2323−23−23000000000000000000000000
χ5444-4-400-2004-4−2i32i3-222−2i32i30000000000−4i4i00−2i32i300000000-22000000002i2i−2i−2i−23−232323000000000000000000000000
χ5544-4-400-2004-42i3−2i3-2222i3−2i300000000004i−4i002i3−2i300000000-2200000000−2i−2i2i2i−23−232323000000000000000000000000
χ5644-4-400-2004-42i3−2i3-2222i3−2i30000000000−4i4i002i3−2i300000000-22000000002i2i−2i−2i2323−23−23000000000000000000000000
χ5744-4-400-200-44−2i32i3-222−2i32i34i4i−4i−4i00000000002i3−2i3000000002-22323−23−23−2i−2i2i2i00000000000000000000000000000000
χ5844-4-400-200-44−2i32i3-222−2i32i3−4i−4i4i4i00000000002i3−2i3000000002-2−23−2323232i2i−2i−2i00000000000000000000000000000000
χ5944-4-400-200-442i3−2i3-2222i3−2i34i4i−4i−4i0000000000−2i32i3000000002-2−23−232323−2i−2i2i2i00000000000000000000000000000000
χ6044-4-400-200-442i3−2i3-2222i3−2i3−4i−4i4i4i0000000000−2i32i3000000002-22323−23−232i2i−2i−2i00000000000000000000000000000000
χ614-44-40044-40000-44-400−2i22i2−2i22i200000000−2i22i2004-4000000000000−2i22i2−2i22i20000−2i22i2−2i22i2000000000000000000000000
χ624-44-40044-40000-44-4002i2−2i22i2−2i2000000002i2−2i2004-40000000000002i2−2i22i2−2i200002i2−2i22i2−2i2000000000000000000000000
χ634-44-4004-440000-44-400−2i22i2−2i22i2000000002i2−2i200-44000000000000−2i22i2−2i22i200002i2−2i22i2−2i2000000000000000000000000
χ644-44-4004-440000-44-4002i2−2i22i2−2i200000000−2i22i200-440000000000002i2−2i22i2−2i20000−2i22i2−2i22i2000000000000000000000000
χ654-44-400-24-400−2i32i32-222i3−2i3−2i22i2−2i22i200000000−2i22i200-2200−2i32i300006−66−6i2−i2i2−i26−66−6i2−i2i2−i2000000000000000000000000
χ664-44-400-24-400−2i32i32-222i3−2i32i2−2i22i2−2i2000000002i2−2i200-2200−2i32i30000−66−66−i2i2−i2i2−66−66−i2i2−i2i2000000000000000000000000
χ674-44-400-24-4002i3−2i32-22−2i32i3−2i22i2−2i22i200000000−2i22i200-22002i3−2i30000−66−66i2−i2i2−i2−66−66i2−i2i2−i2000000000000000000000000
χ684-44-400-24-4002i3−2i32-22−2i32i32i2−2i22i2−2i2000000002i2−2i200-22002i3−2i300006−66−6−i2i2−i2i26−66−6−i2i2−i2i2000000000000000000000000
χ694-44-400-2-4400−2i32i32-222i3−2i3−2i22i2−2i22i2000000002i2−2i2002-2002i3−2i300006−66−6i2−i2i2−i2−66−66−i2i2−i2i2000000000000000000000000
χ704-44-400-2-4400−2i32i32-222i3−2i32i2−2i22i2−2i200000000−2i22i2002-2002i3−2i30000−66−66−i2i2−i2i26−66−6i2−i2i2−i2000000000000000000000000
χ714-44-400-2-44002i3−2i32-22−2i32i3−2i22i2−2i22i2000000002i2−2i2002-200−2i32i30000−66−66i2−i2i2−i26−66−6−i2i2−i2i2000000000000000000000000
χ724-44-400-2-44002i3−2i32-22−2i32i32i2−2i22i2−2i200000000−2i22i2002-200−2i32i300006−66−6−i2i2−i2i2−66−66i2−i2i2−i2000000000000000000000000
χ734-4-444-44000044-4-44-4-422−22−2222000022−220000000000000000−222222−2222−22−222200000000000000000000000000000000
χ744-4-444-44000044-4-44-4-4−222222−220000−2222000000000000000022−22−2222−222222−2200000000000000000000000000000000
χ754-4-444-4-20000-2-222-22222−22−2222000022−2200000000−2i32i300−2i32i3002−2−22−222−2i6−i6−i6i6−i6i6i6−i6000000000000000000000000
χ764-4-444-4-20000-2-222-22222−22−2222000022−22000000002i3−2i3002i3−2i3002−2−22−222−2−i6i6i6−i6i6−i6−i6i6000000000000000000000000
χ774-4-444-4-20000-2-222-222−222222−220000−222200000000−2i32i300−2i32i300−222−22−2−22−i6i6i6−i6i6−i6−i6i6000000000000000000000000
χ784-4-444-4-20000-2-222-222−222222−220000−2222000000002i3−2i3002i3−2i300−222−22−2−22i6−i6−i6i6−i6i6i6−i6000000000000000000000000
χ794-4-44-4440000-4-4-4-444422−22−22220000−2222000000000000000022−22−222222−22−222200000000000000000000000000000000
χ804-4-44-4440000-4-4-4-4444−222222−22000022−220000000000000000−222222−22−222222−2200000000000000000000000000000000
χ814-4-44-44-200002222-2-2-222−22−22220000−222200000000−2i32i3002i3−2i300−222−2−222−2−i6i6i6−i6−i6i6i6−i6000000000000000000000000
χ824-4-44-44-200002222-2-2-222−22−22220000−2222000000002i3−2i300−2i32i300−222−2−222−2i6−i6−i6i6i6−i6−i6i6000000000000000000000000
χ834-4-44-44-200002222-2-2-2−222222−22000022−2200000000−2i32i3002i3−2i3002−2−222−2−22i6−i6−i6i6i6−i6−i6i6000000000000000000000000
χ844-4-44-44-200002222-2-2-2−222222−22000022−22000000002i3−2i300−2i32i3002−2−222−2−22−i6i6i6−i6−i6i6i6−i6000000000000000000000000

Here i is the imaginary unit (i² = −1).